We explore the nonlinear dynamics of a macroeconomic model with resource constraints. The dynamics is derived from a production function that considers capital and a generalized form of energy as inputs. Energy, the new variable, is depleted during the production process and has to be renewed, whereas capital grows with production and decreases from depreciation. Dependent on time scales and energy related control parameters, we obtain steady states of high or low production, but also sustained oscillations that show properties of business cycles. We also find conditions for the coexistence of stable fixed points and limit cycles. Our model allows to specify investment and saving functions for Kaldor's model of business cycles. We provide evidence for an endogenous origin of business cycles if depleting resources are taken into account.